If you believe in something hard enough, it will come true. Like how Santa Claus is apparently real because kids all around the world believe in him. So why not if you focus hard enough on something fictional, it can become real? Certainly no one person has this ability, but what about a whole slew of people? A fandom? All that fanart and fanfics and fansites and hours laboring over something that was never real finally can become a living thoughtform.
So where do we put all these suddenly non-fiction fictionals? You can't have them running around with the general public, so your kid is placed on NEW MOORE until they have accumulated to their new life. A life where they have to accept while they are real now, they weren't before. They need to become functional members of this new society before they're allowed out into the general public, and the island is equipped with counseling and transitional services to help them achieve that normalcy. Welcome to reality rehab!
Unfortunately, the isolated island is vague on the details of this "outside world". What limited information there is available on the world the island is preparing them for is highly censored and closely restricted. Is the real world like Spira, or Middle Earth, or is it like the world from Star Trek? And are they ever actually getting out? Is there anything to get out to? And make no mistake, you want out - the island, while hospitable and reasonably spacious, is a strange place. It seems to respond to the collective mood and mindset of its inhabitants, allowing ideas to mutate the landscape, flora and fauna, and quality of life as you may know it.
On top of that, there's no explanation for where the scientists found you, how you got the the island. There's no way to control or suggest who will appear later. The people looking after you are just as affected by mass thought as the island - so if you think they're benevolent helpers, that's what they'll always be. But if you start to suspect them of being out to get you...
That's all there is for now. Maybe if you believe in an explanation hard enough, you'll get it.